power per unit area received by an observer

I ∝ A

(Wm-2)

represents the motion (oscillation) at one point on the wave 

every point will oscillate in the same manner but start their oscillation at different times

represents a 'snapshot' of a wave

over time it will move on but keep the same shape

transverse waves

travel at the speed of light (3 x 10^8)

gamma<Xrays<UV<Visible<IR<Microwave<TV<Radio

(in terms of wavelength)

there will be both reflection and transmission at the boundary

1. draw normal

2. draw reflected ray

3. draw wavefronts at 90⁰ to ray

1. draw normal

2. draw refracted ray

3. draw wavefronts at 90 degrees to ray

destructive interference

(n + 0.5) x wavelength

constructive interference 

n x wavelength

fired alpha particles at thin gold foil, with a fluorescent screen to detect where they went

- gold is very thin (1000 atoms) and is a large atom

- helium nuclei as it is positively charged and small mass

- most of alpha particles passed through the foil unaffected as most of an atom is empty space

- a significant number of alpha particles had their path deflected as they passed through the foil as the positive charge of an atom is concentrated in the centre and the electrons orbit this nucleus

- some alpha particles bounced straight back from the gold foil as most of the mass of an atom is in the nucleus

emission and absorption spectra

an electron can move between energy levels by either absorbing or emitting a photon

only photons of specific wavengths (and frequency) emitted

white bands on dark

only photons of specific wavelengths (and frequencies) absorbed

set-up by passing light through cold gas (gas absorbs certain wavelengths are leaves remaining colours to be passed onto screen)

strong nuclear force which is balanced by the repulsion between the protons (Coulomb interaction) and is short range and involves neutrons in some way

(larger nuclei have proportionally more neutrons)

each form is known as a nuclide

different number of neutrons but same number of protons

- helium nucleus

- about 5cm range

- stopped by paper

- very high ionising ability (high Ek, positive charge and relatively large mass)

- beta -ve is an electron emitted from the nucleus (neutron--> proton)

- beta +ve is a positive electron or positron emitted from the nucleus (proton --> neutron)

- about 30cm range

- stopped by aluminium

- low ionising ability

- beta -ve particles are accompanied by antineutrinos

- beta +ve particles are accompanied by neutrinos (v)

- electronmagnetic radiation (photons)

- range of hundreds of metres (high energy)

- stopped by thick lead

- very low ionising ability

- always accompanies alpha and beta radiation

sum of the two individual field strengths

(found through vector equations)

g = F/m

F = (GMm)/(r^2)

g = ((GMm)/(r^2))/m

g = (GM)/(r^2)

forces can act at a difference (don't have to be in contact)

force is inversely proportional to r^2

- gravitational field always attract, but electric field can attract or repel depending on charge

- gravitational field depends on mass, and electric field depends on charge

- field lines show force on any mass for gravitational field, and show force on positive charge for electric field

- positive charges

- thumb is motion

- palm is force

- fingers are direction of field

- thumb is current direction

- fingers are field direction

- proportional to its displacement from its equilibrium position

- directed towards its equilibrium position (restoring force)

max occurs at -Xo and +Xo

min occurs at 0

- car suspension

- electric meters with moving pointers (critical)

- some door closing mechanisms (critical)

- microwaves (water resonates)

- radio receivers

- musical instruments

- quartz crystals (clocks)

- poorly designed buildings in earthquakes

- vibrations in machines

low energy --> high energy 

(low frequency --> high frequency)

"more"

energy level does not increase

one electron per photon (when one photon arrives one electron can leave if there is enough energy in photon)

large nuclei broken into smaller nuclei

(two atoms + neutrons + energy)

small nuclei combined if pressure and temperature high enough 

(neutron and energy also emitted)

the amount of energy required to hold a nucleus together

(the amount needed to break it apart)

  N = N_oe^- λt

N_o/2 = N_oe^- λt/2  

0.5 = e^- λt/2

ln(0.5) = - λT0.5

T(half life) = (ln2)/λ

1. find the speed of the electron using

V_e = 0.5 x m x v²

2. find the wavelength using de Broglie formula (p=h/f)

- confirmed the de Broglie hypothesis

- accelerated electrons at a diffraction grating

- experiment showed intereference pattern of electrons

- dimensions of interference pattern matched the expected wavelength of the accelearate electrons

- the distance between the 'antinodes' is that expected by the wavelength of the electron

the total amount of energy emitted by a star per second 

(unit: W)

temperature

size

how bright stars appear to an observer 

(the amount of energy received per second per unit area)

unit: Wm^-2

analysing the spectra of light emitted

the elements in the star will absorb light leaving dark lines in the spectra

radiation pressure = gravitational pressure

(outwards)                  (inwards)

a group of stars held together by gravity

each star is relatively close to each other

theoretical object that is a perfect emitter (and absorber) of radiation

(emit a continuous spectrum of radiation)

dependent on temperature of object

as temperature increases, the peak wavelength gets shorter and the frequency increases

O - blue
B - blue/white
A - white
F - yellow/white
G - yellow
K - orange
M - red

(decreasing in temperature to M) 

magnitude 1

magnitude 6

magnitude 1 = brightest

magnitude 6 = just visible to naked eye

1. parallax

2. spectroscopic parallax

3. cepheid variable

1. can measure up to 100pc using telescopes on Earth

2. above this the able p is too small and is within the uncertainty of the measurement

1. Observe the spectrum of the star

2. Find the peak wavelength of the light emitted

3. Calculate the temperature of the star using Wein's Law

(max wavelength = (2.90 x 10^-3)/T

4. Using the HR diagram to find luminosity of the star (if it is a main sequence star)

5. Measure the apparent brightness from Earth and then calculate the star's distance away 

(b = L/(4pid²)

can only be used for distances up to 10Mpc

(beyond that there is too much error when observing the spectrum)

used for distances greater than 10Mpc

1. Find the period by observation

2. Get the luminosity from the period-luminosity graph

3. Measure apparent brightness on Earth

4. Use b=L/(4pid²) to calculate the distance

- uniform

- static

- infinite (in space and time)

1. based on the reality that the night sky is dark (not bright)

2. if a shell has a thickness (t) and a number of stars per unit volume (n)

No. of stars in shell = area of shell x t x n

= 4πr² x t x n

3. number of stars is proportional to r², and the apparent brightness is proportional to 1/r²

4. no matter the distance the stars would be equally bright and cause the sky to be infinitely bright

IT IS DARK AT NIGHT...

1. created 15 billion years ago (Big Bang)

2. All the matter in today's universe was contained in a single very hot, very dense point --> singularity

4. This rapidly expanded (and cooled) creating space and time

the universe is NOT expanding into space, but creating it

1. Light from galaxies is red-shifted showing they are all moving away from each other --> the universe is expanding

2. Penzias and Wilson (1960s) discovered microwave radiation coming from all directions in space. The wavelength suggests that it is being emitted by an object that has a temperature of 3K (temperature of universe after 15 billion years of cooling)

1. Open Universe (gravity is not strong enough to stop expansion, but gravity slows it dowm)

2. Flat (gravity slows expansion but takes an infinite period of time to stop - if it stopped then gravity would cause it to collapse)

3. Closed (gravity causes the universe to collapse back in on itself)

the density of the universe

1. open: p>p_o

2. flat: p_o

closed: p<p_o

Weakly

Interacting

Massive

Particles

e.g. hypothetical particles